Narayana Pandit
Encyclopedia
Narayana Pandita (1340–1400) was a major mathematician
of India. Plofker writes that his texts were the most significant Sanskrit mathematics treatises after those of Bhaskara II, other than the Kerala school
. He wrote the Ganita Kaumudi in 1356 about mathematical operations. The work anticipated many developments in combinatorics
. About his life, the most that is known is that:
Narayana Pandit had written two works, an arithmetical treatise called Ganita Kaumudi and an algebra
ic treatise called Bijganita Vatamsa. Narayanan is also thought to be the author of an elaborate commentary of Bhaskara II's Lilavati
, titled Karmapradipika (or Karma-Paddhati). Although the Karmapradipika contains little original work, it contains seven different methods for squaring numbers, a contribution that is wholly original to the author, as well as contributions to algebra and magic square
s.
Narayanan's other major works contain a variety of mathematical developments, including a rule to calculate approximate values of square roots, investigations into the second order indeterminate equation
nq2 + 1 = p2 (Pell's equation
), solutions of indeterminate higher-order equations
, mathematical operations with zero
, several geometrical
rules, and a discussion of magic squares and similar figures. Evidence also exists that Narayana made minor contributions to the ideas of differential calculus
found in Bhaskara II's work. Narayana has also made contributions to the topic of cyclic quadrilateral
s.
Narayana is also credited with developing a method for systematic generation of all permutations of a given sequence.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
of India. Plofker writes that his texts were the most significant Sanskrit mathematics treatises after those of Bhaskara II, other than the Kerala school
Kerala school
Kerala school may refer to*Kerala school of astronomy and mathematics, a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, South India which flourished between the 14th and 16th centuries CE....
. He wrote the Ganita Kaumudi in 1356 about mathematical operations. The work anticipated many developments in combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
. About his life, the most that is known is that:
Narayana Pandit had written two works, an arithmetical treatise called Ganita Kaumudi and an algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
ic treatise called Bijganita Vatamsa. Narayanan is also thought to be the author of an elaborate commentary of Bhaskara II's Lilavati
Lilavati
Lilavati was Indian mathematician Bhāskara II's treatise on mathematics. It is the first volume of his main work Siddhānta Shiromani, Sanskrit for "Crown of treatises," alongside Bijaganita, Grahaganita and Golādhyāya.- Name :The name comes from his daughter Līlāvatī...
, titled Karmapradipika (or Karma-Paddhati). Although the Karmapradipika contains little original work, it contains seven different methods for squaring numbers, a contribution that is wholly original to the author, as well as contributions to algebra and magic square
Magic square
In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...
s.
Narayanan's other major works contain a variety of mathematical developments, including a rule to calculate approximate values of square roots, investigations into the second order indeterminate equation
Indeterminate equation
An indeterminate equation, in mathematics, is an equation for which there is an infinite set of solutions; for example, 2x = y is a simple indeterminate equation. Indeterminate equations cannot be directly solved from the given information...
nq2 + 1 = p2 (Pell's equation
Pell's equation
Pell's equation is any Diophantine equation of the formx^2-ny^2=1\,where n is a nonsquare integer. The word Diophantine means that integer values of x and y are sought. Trivially, x = 1 and y = 0 always solve this equation...
), solutions of indeterminate higher-order equations
Degree of a polynomial
The degree of a polynomial represents the highest degree of a polynominal's terms , should the polynomial be expressed in canonical form . The degree of an individual term is the sum of the exponents acting on the term's variables...
, mathematical operations with zero
0 (number)
0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...
, several geometrical
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
rules, and a discussion of magic squares and similar figures. Evidence also exists that Narayana made minor contributions to the ideas of differential calculus
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
found in Bhaskara II's work. Narayana has also made contributions to the topic of cyclic quadrilateral
Cyclic quadrilateral
In Euclidean geometry, a cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. Other names for these quadrilaterals are chordal quadrilateral and inscribed...
s.
Narayana is also credited with developing a method for systematic generation of all permutations of a given sequence.